With bootstrapping you can obtain the variability of various summary statistics. Recently I came across the Bayesian bootstrap (http://www.sumsar.net/blog/2015/07/easy-bayesian-bootstrap-in-r/). I was curious how large the difference are between the Bayesian and Normal bootstrap. As difference I focus on variability of the mean difference between two hypothetical normal distributions (x = N(0.1, 1) and y = N(0, 1)) with corresponding 95% confidence and credibility intervals (?). I played around with various extremes of the sample sizes (n = 3 or n = 1000). My expectations were that the results from the Bayesian bootstrap would be more conservation (e.g. wider credibility intervals (?)) than that of the normal bootstrap, this seems not to be the case. My question is why?
I am sorry for my ignorance regarding the Baysian bootstrap principle and I am also not certain if the 2.5% and 97.5% can be named credibility intervals. I often like to say that I just obtained the 2.5% and 97.5% of of the bootstrap to avoid using these terms. I think I might do something incredibly wrong here.
Generally, the closer form of the model and fewer sources of uncertainty cause more accurate estimates and thus the lower confidence interval.
Babak Jamshidi Yes indeed, but the differences are very minor in my opinion. At least, when I would consider the summary statistics, gradients, variables etc. I work with. Perhaps this minor difference might be very important in other field e.g. micro-biology or biomedical sciences. The author also mentions: "The classical non-parametric bootstrap is pretty similar to the Bayesian bootstrap".
Well Wim if you have decided on the answer why ask the question? D. Booth
David Eugene Booth Freedom, curiosity, ignorance, stupidity and I have no filter at all. Also, I am not really sure if I am searching for an answer? On RG there is not obligation for someone to answer or find it a good/valuable question. Perhaps someone gives a really short straightforward answer that improves my understanding or changes my view and let me look at it differently (or perhaps not?). The term answer also seems so definitive. But, if there is only on single publication on one specific topic/question this would also be sufficient as it gives an answer.
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